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Question
Determine the volume contraction of a solid copper cube, 10 cm on an edge, when subjected to a hydraulic pressure of 7.0 ×106 Pa.
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Solution 1
Length of an edge of the solid copper cube, l = 10 cm = 0.1 m
Hydraulic pressure, p = 7.0 ×106 Pa
Bulk modulus of copper, B = 140 × 109 Pa
Bulk Modulus, `B = p/((triangle V)/V)`
Where
`(triangle V)/V` = Volumetric strain
ΔV = Change in volume
V = Original volume.
`triangleV = (pV)/B`
Original volume of the cube, `V = beta`
`:.triangle V = (pl^3)/B`
`= (7xx10^6xx (0.1)^3)/(140xx10^9)`
= 5 x 10-8 m3
= 5 x 10-2 cm-3
Therefore, the volume contraction of the solid copper cube is 5 × 10–2 cm–3.
Solution 2
Here a side of copper cube a = 10 cm, hence volume V = a3 = 10-3 m3 , hydraulic pressure applied p = 7.0 x 106 Pa and from table we find that bulk modulus of copper B = 140 G Pa = 140 x 109 Pa.
Using the relation `B = p/((triangle V)/V)` we have decreased in
volume `triangle V = (PV)/B`
`:. triangleV = (7.0xx10^6xx10^(-3))/(140xx10^9) = 5xx 10^(-8) m^3 = 5 xx 10^(-2) cm^3`
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